Welcome to the module on Mathematical modelling within BIOL3360! In this module you will learn why and how to construct mathematical models, how to analyse them, how to implement them in R, and how to interpret the results.

Most of the examples for models will be drawn from the fields of ecology, infectious disease epidemiology, and evolution. This does not mean that mathematical models are not important in other areas of biology (they are!), it merely reflects personal taste and the belief that ecological and epidemiological models in particular are easier to relate to for students with different backgrounds than, say, models for developmental or physiological processes.

These lecture notes will closely follow the content of the lectures. I will not use slides during the lectures and there is no textbook that I will follow, so the lecture notes will be your main source of reference for this module. The notes are structured according to lectures. Each of the five chapters concludes with a number of exercises. We may go through some of these exercises during the lecture, but it is important that you review the notes for each lecture and go through the exercises by yourself or with others outside the lectures and pracs. Mathematical modelling can only be learned by actually doing it.

This module assumes only very little background in mathematics. You should be familiar with the concept of a function, you should be comfortable working with exponentials and logarithms, and you should know the basics of calculus (in particular, derivatives). We will also cover models that involve differential equations, but no prior knowledge about differential equations is assumed. For the last lecture, some basic knowledge of probability theory will be assumed. Some limited knowledge of coding in R is also required, but you should have come across everything you need in the previous module on statistics as well as other courses that you took. You should know what variables and functions are in R, you should be comfortable working with (especially indexing!) vectors and matrices, you should have some knowledge of if statements and loops (for and while), and you should be able to plot your results.

In this online version of the lecture notes we have included four apps, created by your tutor Nicole Fortuna specifically for this course. These apps illustrate important concepts of the material in an interactive manner. Unfortunately the apps don’t run directly in the online version of this book but you can copy-paste the code into R or RStudio and then run it. All apps require the library shiny to be installed.

BIOL3360 is a fairly new course. This is the third edition of these lecture notes on mathematical modelling, and the first time these notes have been presented in an online format. Therefore, there might still be typos and errors of all sorts in the text and equations - don’t take anything for granted! If you do spot an error, please do let me know.

Jan Engelstädter
April 2019